The northern end of the lagoon is a excellent place for Kite surfing.
http://www.auberge-des-nomades-du-sahara.com/ (french only)
Staying in Dakhla is cheaper but you will have a transportation problem.
If you come with a camper there is also a trailerpark.
From the big empty square, cross the busy road, and in front of you, you'll find the old Spanish Cathedral. I have to say I quite like this style of Spanish desert architecture, all straight lines and curves and domes, and it reminded me of the cathedral in Laayoune. Sadly, this doesn't seem to be in use any more and is locked. Over the road is a garden with shade provided by palms and some unusual concrete...erm...things.
Further north, you'll soon come to a new square. Moroccan city planners seem to like these big empty squares, and Dakhla's is exactly that...empty. Nobody bothers going there, preferring the busier, livelier and more fun small square by the budget hotels and souqs. A tent stands in one corner for shade, bizarrely with no bench underneath it to sit on, while in the opposite corner, a rare monument...one in the shape of the Dakhla Peninsula. When approaching the monument, take a look at the tiles on the ground...they too form a map of the peninsula, almost like a tiled shadow of the monument.
Quite tricky to find, what looks like the oldest part of Dakhla is worth seeking out, as it has a very different atmosphere to the rest of the town. Somewhere between the Ensemble Artisanal (a few workshops and jewellery stores, but often closed) and the old souq, look out for one of the narrow backstreets, mostly with sand underfoot instead of tarmac. The houses on these backstreets are noticeably older and more decayed than anything else in Dakhla, are one storey with decorated rooftops, and many have been painted bright colours. It doesn't feel like Morocco, and many of the people living here are indeed not Moroccan but migrants from further south. A sign in Arabic points to "al-masjid al-'ateeq", the ancient mosque, although nothing in Dakhla is really that ancient. It's a tiny one-room affair, very easy to miss. As a non-muslim, I couldn't enter, but there's nothing to stop you from walking past.
A much simpler whitewashed mosque, possibly built by the Spanish, stands at the heart of Dakhla. I think I preferred this one to the new one, as it suits Dakhla more, perhaps more in keeping with the style of other buildings in the centre...low-rise, white, not too complicated.
This mosque is the start of the nightly parade of people, who wander between here and the square a few blocks north by the budget hotels, chatting, drinking coffee and shopping. I arrived on a Sunday, and the place was heaving with people, and the second and third nights were still busy.
If it's cafes you're after, then you've got a wide choice, as long as you're male. A few new places have opened opposite the mosque, brightly decorated in orange, and are prime spots for people-watching, as is the big outdoor patisserie/cafe a bit further up. The liveliest place, though, is the square between the sea and the souq, where most of the budget hotels are (Atlas, Sahara, Riad, etc.). Not quite Djemaa el Fna, it is nevertheless crowded with stalls and tents, with the odd musician. Foodwise, there's a few grills smoking away in the corner, popcorn and icecream, and once you're done shopping and eating, it must be time for another coffee, so head to the Cafe Al Jazeera at the far end of the square, which also overlooks the seafront.
A brand new mosque has been built south of the town centre, almost as if the government is trying to move away from the narrower older streets and create a new centre for Dakhla, with the mosque as its focal point. It's an impressive building, with a colourful minaret. Beside it is a park, especially popular with women and children in the evening, and full of food carts selling snails, chickpeas, soup and popcorn.
Not a beach by anyone's standards, nevertheless, Dakhla's four sections of seafront promenade are worth walking along, especially late afternoon and evening, when they're at their busiest. Nothing really to see, but it's quite a long walk from the new mosque up to the northern part of the seafront, especially in high winds. The sun can be very strong (in January, it was 28 degrees according to the little temperature sign outside one of the banks, and in summer it must get very hot indeed), and there isn't much in the way of shade, save for a few tent-like structures. There is access down to the sea...you have to vault the railing and clamber down the rocks, although there isn't really much of an incentive to do so. Unfortunately, the rare patches of sand down below are rubbish strewn and attract rats.
There are a couple of cafes to stop in to take in the views, such as Samarqand and the Bab el Bahar Hotel, which is quite a striking piece of architecture in itself...all you can see from the road is the domes on the roof, which are at pavement level...the hotel itself is underneath, right on the sea. There are also cheaper cafes on the other side of the road, where you can enjoy a 5 dirham coffee and people watch.